Mohammed Absullah Al-Walid, 24, deputy commander of Zinjibar's 'Popular Committee' with his fighters in Aden, Yemen, July 11 2012. Armed groups of citizens who rose against Al Qaeda known as popular committees were key to the Yemeni government's ability to reclaim Abyan province from AQAP.

Could tiny, impoverished Yemen be showing the way to vanquish al-Qaeda? That’s the subject of my latest article in the current issue of TIME magazine. This summer, unnoticed by most of the world, Yemeni troops reclaimed territory that for over a year had been controlled by the terrorist network’s local franchise, known as al-Qaeda in the Arabian Peninsila (AQAP). The fighting was intense and bloody, but in the end the jihadists were soundly beaten. Many were killed, and those who fled are now finding it much harder than before to find shelter among tribesmen in the more remote parts of the country.

The U.S. can claim — but is being careful not to — some of the credit, since American drones played a part in the battle. But the boots on the ground were Yemeni, and it was they who did most of the hard fighting. In meaningful ways, this was a victory for the Arab Spring: the uprising removed Ali Abdallah Saleh, Yemen’s longstanding dictator, from office, and his elected replacement, President Hadi, has made defeating AQAP a high priority.

It helped, too, that a national consensus had evolved about the danger AQAP presents to Yemen. Only a couple of years ago, many Yemenis thought the jihadists were America’s problem, not their own. But when AQAP seized a swath of territory in the southern province of Abyan, that delusion could no longer be sustained. Ruling much like Afghanistan’s Taliban, AQAP imposed a harsh interpretation of Islamic law on towns like Zinjibar and Jaar: the population responded by fleeing. Tens of thousands flocked to the port city of Aden, where their presence undermined the jihadists claim to being a popular movement.

The refugees are now returning home, and Hadi’s government has been buoyed by the military victory. But the war is not over. Many AQAP fighters remain at large, and they have returned to older tactics of suicide attacks. One bomber killed over 100 soldiers at a military parade in Sana’a on May 21. If it demonstrated the jihadists continued threat, it also exposed their desperation. And to many Yemenis, it only underlined the new recognition that AQAP is not just America’s problem: it’s theirs, too.